Almost never do you hear of "reel grease", it's always an oil. Can't recall which reel I had that said "USE NO GREASE".

I have used the Penn oil for years and had good result.
Gun oil is OK but the reel oils are more waterproof I think. Synthetics are good, super lube is too but be aware of silicone base stuff. Once it gets cold and hard you are stuck with a sticky reel mechanism. You'll be sorry you used the wrong stuff.